Patient-specific characterization of the invasiveness and proliferation of low-grade gliomas using serial MR imaging and a mathematical model of tumor growth

Low-grade gliomas (LGGs) represent a significant proportion of hemispheric gliomas in adults. Although less aggressive than glioblastomas (GBMs), they have a broad range of biologic behavior, and often a limited prognosis. The aim of the present study was to explore LGG growth kinetics through a combination of routine MRI imaging and a novel adaptation of a mathematical tumor model. MRI imaging in 14 retrospectively identified grade II LGGs that showed some tumor enhancement was used to assess tumor radii at two separate time-points. This information was combined with a reaction‑diffusion partial-differential equation model of tumor growth to calculate diffusion (D) and proliferation (ρ) coefficients for each tumor, representing measures of tumor invasiveness and cellular multiplication, respectively. The results were compared to previously published data on GBMs. The average value of D was 0.034 mm2/day and ρ was 0.0056/day. Grade II LGGs had a broad range of D and ρ. On average, the proliferation coefficient ρ was significantly lower than previously published values for GBM, by about an order of magnitude. The diffusion coefficient, modeling invasiveness, however, was only slightly lower but without statistical significance. It was possible to calculate detailed growth kinetic parameters for some LGGs, potentially providing a new way to assess tumor aggressiveness and possibly gauge prognosis. Even within a single-grade (WHO II), LGGs were found to have broad range of D and ρ, possibly correlating to their variable biologic behavior. Overall, the model parameters suggest that LGG is less aggressive than GBM based primarily on a lower index of tumor proliferation rather than on lesser invasiveness.